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Digital fingerprinting with accelerometry data

Digital fingerprinting with accelerometry data

Big picture: time series to scalar predictors

Details

For each second and each person:

• Obtain joint distribution of acceleration and lag acceleration for a series of lags

• Either:

  • Obtain summaries of the joint distribution
  • Use full joint distribution directly in functional regression

• We walk through the process for one second, person, and lag to illustrate the process

Obtain joint distribution of acceleration and lag acceleration

Obtain joint distribution of acceleration and lag acceleration

Obtain joint distribution of acceleration and lag acceleration

Obtain joint distribution of acceleration and lag acceleration

Obtain joint distribution of acceleration and lag acceleration

Derive predictors from joint distribution

Derive predictors from joint distribution

Derive predictors from joint distribution

Derive predictors from joint distribution

Derive predictors from joint distribution

Repeat for multiple lags

Repeat for all seconds

Repeat for all people

Fit models

Fit models

::: {.incremental} + \(n\) models, one for each person + Model \(j\) predicts probability that second \(i\) is from person \(j\) + Max prediction across all models is the predicted person for that second + Models include: logistic regression w/ variable selection, lasso, random forest, XGBoost, etc.

::: {.incremental}

Detour: functional regression approach

Detour: functional regression approach

Detour: functional regression approach

Detour: functional regression approach

Detour: functional regression approach

\[\text{logit}(p_{ij}^{i_0}) =\beta_0^{i_0} + \int_{u=1}^S\int_{s=u}^SF_{i_0}\{ v_{ij}(s), v_{ij}(s-u), u\}dsdu \]

\(u = 1, \dots, S = 100\) (number of observations per second)

\(v_{ij}(s)\) = acceleration at centisecond \(s\) for subject \(i\) in second \(j\)

\(F(\cdot, \cdot, \cdot)\): trivariate smooth function

“Fingerprints” summarize predictors for a given lag and are different across individuals

“Fingerprints” summarize predictors for a given lag and are different across individuals

The method works!

Train/test paradigms, visualized

So what?

Detour through NHANES: open source step counting

Detour through NHANES: open source step counting

Detour through NHANES: open source step counting

Detour through NHANES: open source step counting

Detour through NHANES: survey-weighted functional regression

Another question motivated by NHANES: how are physical activity patterns associated with covariates like age, sex?

Detour through NHANES: survey-weighted functional regression

We can answer this question with function on scalar regression (FoSR):

Implementation: fast univariate inference (FUI)

\[\mathbb{E}[\mathrm{MIMS}_i(s)] = \beta_0(s) + \beta_1(s)\mathrm{gender}_i + \beta_2(s)\mathrm{age}_i \]

Detour through NHANES: survey-weighted functional regression

But: NHANES is not a simple random sample Are our estimates valid for population-level inference?

Detour through NHANES: survey-weighted functional regression

\(\texttt{svyfosr}\): first survey-weighted functional regression implementation in R

Digital fingerprinting with hemodynamics data

Preliminary hemodynamics work

Summarizing times in fine-grained ranges of mean arterial pressure and cardiac index or central venous pressure